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Home , Fermi paradox, Neocatastrophism, Rare Earth hypothesis

Serb. Astron. J. } 176 (2008), 71 - 79 UDC 52–37 DOI: 10.2298/SAJ0876071V Preliminary report

NEOCATASTROPHISM AND THE ASTROBIOLOGICAL LANDSCAPE

B. Vukoti´cand M. M. Cirkovi´c´

Astronomical Observatory Belgrade, Volgina 7, 11160 Belgrade, Serbia E–mail: [email protected]

(Received: February 13, 2008; Accepted: April 1, 2008)

SUMMARY: The number and distribution of habitable in the Milky Way is one of the foremost problems of contemporary astrobiological research. We investigate the effects of applying general neocatastrophic paradigm to the of the . In this paper, we investigate the limits of simple, 1- dimensional astrobiological models, and consider the role of regulation mechanisms in shapening the ”astrobiological landscape”. We show that the transition from predominantly gradualist to predominantly (neo)catastrophist history of our Galaxy leads to the build-up of large-scale correlations between habitable sites, offering possible keys to such important problems as Carter’s ”anthropic” argument and Fermi’s paradox. In addition, we consider the possibilities for extending the present class of models into spatially realistic 3-dimensional case via probabilistic cellular automata.

Key words. – methods: numerical – Galaxy: evolution – extraterres- trial

How many kingdoms know us not! Cirkovi´c2004a,´ Blair et al. 2008), as well as occa- Blaise Pascal, Thoughts, 207 sional criticism (Prantzos 2007). On the balance, it seems that it has offered a useful framework for for- mulation of some of the most general, far-reaching ideas about the emergence of (biogenesis) and 1. INTRODUCTION intelligence (noogenesis) on the Galactic scale. In the present paper, we study the class of simplest, 1- The concept of the Galactic Habitable Zone dimensional astrobiological models of GHZ, examine (henceforth GHZ) emerged as one of the crucial their limits of application and discuss a particular hypothesis about the general astrobiological evolu- terms of the contemporary astrobiological research tion in the Milky Way, namely the neocatastrophic (often dubbed, with much justification, ”the astro- view. biological revolution”). Starting with the pioneer- The present approach seeks to join the older ing paper by Gonzalez et al. (2001), the concept tradition of more specialized SETI-oriented models, experienced significant elaboration and generaliza- as exemplified by the studies of Newman and Sagan tion (e.g. Lineweaver et al. 2004, Gonzalez 2005, (1981), Fogg (1987) or Landis (1998) with the recent

71 B. VUKOTIC´ and M. M. CIRKOVI´ C´ astrobiological developments, notably GHZ elabora- timescale is much larger than the astrophysical one, tions and the re-emergence of (neo)catastrophic view thus making the evolution of life and intelligence else- of the large-scale biospheric evolution. Some results where correspondingly improbable. of this kind of modeling have been presented by 3. The argument from biological contingency Vukoti´cand Cirkovi´c(2007,´ henceforth Paper I) and (Simpson 1964, Mayr 1993): the part of biological Vukoti´c(2008, henceforth Paper II). The application morphospace containing intelligent beings capable of of these results to resolving the famous Carter’s ar- SETI-like communication is so minuscule in volume, gument against extraterrestrial intelligence has been that even if all habitable planets in the Galaxy are ´ indeed inhabited by life of some kind, SETI will still presented in Cirkovi´cet al. (2008). Finally, the res- be condemned to failure. olution of Fermi’s paradox through the phase transi- The ”Big Three” arguments against SETI tion scenario encapsulated by these models is pre- have played a large role not only in academic discus- sented in Cirkovi´cand´ Vukoti´c(2008). Here, we sions about these topics, but also in its wider cultural would like to elaborate upon the applicability con- and societal perspectives (i.e. Mayr 1993), includ- ditions of such stochastic models, properties of the ing the US government budget cuts for SETI. They relevant regulation mechanisms, as well as their em- have been influential in formulating the controver- bedding into a more general and realistic 2-D and sial, but very popular in the astrobiological circles, 3-D astrobiological modeling framework. ”rare ” hypothesis (Ward and Brownlee 2000, Conway Morris 2003). As has been argued elsewhere ´ ´ 2. MOTIVATION FOR 1-D (Cirkovi´c2004ab, Cirkovi´cet al. 2008), these ar- guments are inconclusive, but very instructive and NEOCATASTROPHIC MODELS should present a strong motivation for the develop- ment of theoretical SETI. We know very little about the details of what The present approach can be regarded as a could be dubbed ”astrobiological dynamics”, namely way of direct simulation testing of the famous Drake the laws governing biogenesis and noogenesis, the de- equation, developed by for the first pendence of the speed of evolution and size of the SETI symposium in 1961. In a sense, it is one of the morphological space on the environmental conditions very rare theoretical SETI results. Although there in general case, etc. Even in such situations, as for is no canonical form of the , and the instance the history of many-body physics shows us, expression quoted by various authors is often depen- one can learn a great deal about the large-scale, col- dent on the desired result of the analysis, we use the lective behavior of the system through Monte Carlo following form (e.g. Shklovskii and Sagan 1966, Wal- simulations, which neglects local details and gives ters et al. 1980): information only on the most general trends. Along the line of the same idea, we have constructed a se- N = R∗fgfpneflfifcL, (1) ries of 1-dimensional models, where we are only in- terested in the number of inhabited planets in any while keeping in mind that other equivalent forms given epoch, while the local biological timescales are exist. In this expression, the symbols have the fol- chosen at random from a sufficiently broad tempo- lowing meanings: ral interval. Specifically, we have been motivated by the idea of ”simulating” the important Carter’s N = the number of Galactic with anthropic argument against extraterrestrial intelli- which communication is possible. R∗ = mean rate of formation in the gence (Carter 1983). Carter’s argument is one of the Galaxy, three ”classical” (in the sense of being discussed in fg = fraction of suitable for supporting most of the SETI-era starting from early 1960s) anti- life, SETI arguments. These are (in somewhat simplified fp = fraction of stars with planetary systems, terms): ne = number of planets per 1. Fermi’s paradox (Brin 1983, Jones 1985, with conditions ecologically suitable for the origin Webb 2003): Any early spacefaring and evolution of life, should have colonized the entire Galaxy, includ- fl = fraction of suitable planets where life orig- ing the and Earth by this late time inates and evolves into more complex forms, in Galactic history. This is not what we observe fi = fraction of planets bearing life with intel- (”Great Silence”). ligence, 2. Carter’s anthropic argument (Carter 1983, fc = fraction of planets with intelligence that 1993, Livio 1999): If biological and astrophysi- develops a technological phase during which there is the capability for an interest in interstellar commu- cal timescales determining the evolution of life and nication, intelligence are independent, we have a posteri- L = mean lifetime of a technological civiliza- ori Bayesian reasons to believe that the biological tion.

72 AND THE MILKY WAY ASTROBIOLOGICAL LANDSCAPE

Drake’s equation is usually used as a rule- Annis (1999a) noticed that gamma-ray bursts of-thumb estimate in order to assess feasibility of (GRBs) seem to satisfy all three desiderata. These SETI projects covering fixed number of targets. It strongest explosions in the have several ways has many weaknesses, repeatedly elaborated by both of adversely influencing over a large range -pessimists and optimists (e.g. Lem 1977, of distances within their host galaxies (Thorsett Brin 1983, Gould 1987, Fogg 1988, Cirkovi´c2004b).´ 1995, Scalo and Wheeler 2002, Melott et al. 2004). However, in order to assess validity of its estimates, The decrease of their frequency in time, roughly fol- we need to compare them with a more detailed nu- lowing an exponential trend, recoverable from cosmo- merical model and, since the only value we are in- logical observations, makes the astrobiological clocks terested in is the total number of targets N, the 1-D in GHZ running longer and longer without reset. models like the one we propose are satisfactory can- This, in turn, virtually guarantees that at some point didates. Various f-parameters in Drake’s equation there will be a sudden ”phase transition” between are, essentially, filters for habitability; a large part mostly dead Galaxy and the Galaxy teeming with of them can be thought of as regulation mecha- life (and, presumably, viable SETI targets). It is this nisms influencing the local evolution on habitable aspect of Annis’ conjecture rather than the specific planets in GHZ. Astronomical factors in Eq. (1) are regulation mechanism he advocated that renders his nowadays reasonably well-understood due to the im- theoretical approach genuinely novel. mense progress in astrobiological research in recent Obviously, the increase in level of technologi- ; notably, this applies to R, fg, fp and, in sig- cal sophistication which, in accordance with our as- nificantly lesser degree, ne. As a result of such de- sumptions, is just the extension of the increase in velopment, main uncertainties left lie with biological biospherical complexity will—if unimpeded for quite and ”sociological” factors, namely fl, fi, fc and – in a brief period beyond the present level—lead particular – L. to the security of intelligent community (and, indeed, most of the domicile ) against the GRB threat. There are two aspects of such development. 3. A SURVEY OF NEOCATASTROPHIC The first, astronomical, will enable accurate surveil- REGULATION MECHANISMS lance on all potential Galactic GRBs (that is, rel- ativistic binaries and hypernovae-progenitors), thus enabling accurate prediction of the event with a large While the detailed discussion of astrobiologi- temporal margin. The second, mitigating, will en- cal regulation is beyond the scope of the present pa- able adequate planetary and structural protection, per, it is important, at least, to consider some back- including macroengineering projects; cf. Badescu et ground information underlying any neocatastrophic al. (2006). This is probably only of the order of model. We envisage (quasi)equilibrium GHZ where decades in the future from the point of view of the astrobiological ”clocks” tick at various rates on dif- present human civilization. ferent planets, but are subject to temporally and Among other regulation mechanisms occasion- spatially correlated ”resetting events”. ”Resetting ally proposed in the literature, one may mention: events” could, in principle be uncorrelated as well, but we are more interested in a subset which can 1. Galactic . The claimed periodicities be correlated over large spatial volume. Those are in biological mass extinctions (Raup and Sepkoski the global regulation mechanisms, because they in- 1986, Raup 1999) has provoked a lot of discussion, fluence a large part or the whole GHZ. It is impor- and the one of less controversial explanations has tant to understand that only global mechanisms can been the hypothesis of Galactic tides perturbing lo- ensure stability of equilibrium states. This is re- cal Oort clouds (e.g. Delsemme 1987, Matese and lated to what is in classical SETI studies called ”non- Whitmire 1996). The case for periodicities has re- exclusivity” of explanations for the ”Great Silence”, cently come under severe criticism (Stigler and Wag- i.e. the absence of visible manifestations of very ad- ner 1987, Jetsu 1997, Jetsu and Pelt 2000), to which vanced extraterrestrial civilizations (Brin 1983). we shall return below. Thus, the desiderata for viable mechanisms of 2. Spiral-arm crossings (Shaviv 2002ab, Gies global regulation are: (i) sufficient lethality, (ii) a and Helsel 2005), which could influence climate, and large volume of effect (comparable to GHZ volume), consequently, cause global catastrophes on Earth-like and (iii) secular evolution, i.e. the decrease of av- planets everywhere in GHZ; this is one more form in erage risk with time. The requirement (ii) is the which the notion of ”coherent catastrophism” (Asher rationale for using the term ”global”, while bearing et al. 1994) can be effectively generalized. in mind that this does not necessarily imply that 3. bombs. Collar (1996) has pro- the entire GHZ is affected, just a substantial part posed that even ”normal” stellar-collapse of it. The last property enables phase transition to might play an important biological role and poten- occur, obviating the ”anthropic” question why have tially cause mass extinctions. we emerged at precisely this point in Milky Way’s 4. Magnetars (e.g. Komissarov and Barkov history? (More on the phase transition itself in the 2007) were suggested as origin of high-energy cosmic forthcoming study Cirkovi´cand´ Vukoti´c2008.) rays in a manner similar to supernovae and GRBs.

73 B. VUKOTIC´ and M. M. CIRKOVI´ C´

5. Nuclear outbursts. Clarke (1981) has sug- to explain the long delay between the epoch of bio- gested in an early version of the phase-transition genesis and the of multicellular model that the large-scale environment is decisive life which, at least on Earth, was a precondition for in emergence or not of a viable SETI target. Clarke noogenesis. We feel that (as elaborated above) GRBs based his view on the idea, somewhat fashionable offer a plausible explanation for such a temporal pat- in late 1970s, that the nucleus of the Milky Way tern. can undergo Seyfert-like recurrent bursts of activ- Apart from global, there certainly exist local ity (e.g. Sanders and Prendergast 1974, van Bueren regulating mechanisms, like the impacts of comets 1978, Clube 1978, Giler 1983). A variation on this and asteroids, for quite some time the prime ”sus- theme is the theory of LaViolette (1987) postulating pects” for causes of the palaeontological mass ex- ”volleys” of cosmic rays from the . tinctions (e.g. Raup 1991, 1994, 1999), if we do not ascribe them to the Galactic effects. Galactic ef- These (and other conceivable) mechanisms are fects of this type are also uncorrelated, so they can not, of course, of equal credibility and importance. be regarded as playing the role of random ”noise” It is certain, for instance, that the possible lethal in- in the astrobiological clocks resetting. This complex fluence of neutrinos has been vastly overestimated by behavior should not be surprising at all. In fact, it Collar (1996), or that even the relatively close events is reasonable to assume that galactic ecology is, like like the terminal explosion of Eta Carinae are likely the terrestrial one, made of complex nested systems to have much smaller influence on the terrestrial bio- simple in an overview, but incredibly complex in de- sphere than it was envisaged earlier (cf. Thomas tail. et al. 2008). Nuclear outbursts are much harder to Symbolically, we can write: quantify, but it seems that they do not present a Regulation mechanisms = GRBs + significant threat in the GHZ either. We make the Galactic tides + ... list here just in order to emphasize how these have been discussed (and critically assessed) in the liter- Building of complete ”risk function” for all various kinds of risks is undoubtedly a hard task, ature thus far, while the mainstream astrobiological but its completion could open quite new vistas for discourse remained rather gradualist in its outlook. astrobiological modeling in the future. The issue of periodicity of certain of the reg- We could add any ”sociological” explana- ulation mechanisms has repeatedly surfaced in the literature, after the seminal paper of Raup and Sep- tion in Brin’s (1983) catalog to this category of koski (1984), claiming a statistically significant peri- local regulating mechanisms. All suggested vari- ations on the theme of self-destruction of tech- odicity in the data on marine extinction of terrestrial nological civilizations, through nuclear (/chem- species. The underlying idea has been that the aster- ical/biological/nanotechnogical/...) warfare or oidal/cometary impacts, to which most of the mass through ecological devastation of its environment extinction episodes have been ascribed, are in turn (including the ultimative—and highly speculative— triggered by an astronomical ”clock” with period var- iously claimed to be about 30 Myr. Recently, Rohde ecological catastrophes like the vacuum phase transi- and Muller (2005) have reworked the periodicity hy- tion or creation of destructive strangelets), belong to pothesis with much more comprehensive data, de- this category. and rates for these local tecting a significant period of longer duration, ∼ 140 mechanisms are much harder to classify (as admitted Myr. In recent years, it seems that the hypothesis of by Newman and Sagan, among the SETI optimists), periodicity has been repeatedly criticized (e.g. Jetsu but in the present model it is not really necessary. and Pelt 2000). These local influences play only a role of small per- In fact, the weakening of the case for ”strong” turbations in the overall picture, at least until the periodicity is convenient from the point of view of the technological civilization capable of making itself im- mune to the kind of global catastrophes considered present model. Some periodicities are expected to be emerges. generated by periodical secondary regulating mech- The overall regulatory complex (global + lo- anisms which do possess intrinsic regularity (like the cal influences) is capable of explaining why we do Galactic tides and/or spiral-arm-crossing climatic ef- not observe extragalactic ETI signals or traces of fects), but the main signal is expected to originate advanced astroengineering activities. Since the vol- in intrinsically aperiodic events, that is, both types ume of space sampled by extragalactic observations of GRBs. is much larger than that of Galactic studies, it would Thus, we can partially reject the criticisms of seem natural at first glance to expect even more Abbas and Abbas (1998) directed at Collar’s hypoth- rare events, like the emergence of Kardashev’s Type esis (see ”Neutrino bombs” subsection above). We do III civilizations, observable from afar (e.g. Annis not need to explain periodicity of extinction events, 1999b). However, there is a catch here; the true vol- since we do not believe that the case for periodic- ume is 4-volume of spacetime, and it is severely lim- ity in the strong sense has been convincingly made. ited by the finite velocity of light. We assume that What we do need to explain is the average spacing the same regulatory mechanisms are acting in other between the extinction events sampled over a suffi- spiral galaxies in the same manner as in the Milky ciently long period of terrestrial history, coupled with Way. possible weak periodic signal. In addition, we need 74 NEOCATASTROPHISM AND THE MILKY WAY ASTROBIOLOGICAL LANDSCAPE

Finally, a local non-destructive regulation zone” of a GRB, and (2) describing more mechanism which can be of importance is hypotheti- complex effects dealing with the physics and ecology cal interstellar (for a historical overview, of the extinction mechanism. It is important to keep see Raulin-Cerceau et al. 1998). The most radi- in mind that both these effects can be subsumed into cal version of the idea is the hypothesis by Hoyle a single quantity in simple models, but more sophisti- and Wickramasinghe, developed in the monograph cated future work to be discussed in the next section of Hoyle et al. (1986), that some terrestrial epi- will include multiple probability parameters. Output demics are caused by microorganisms delivered to is the number of habitable sites achieving noogenesis Earth via comets’ tails. However, even the more at least once (in this way we avoid overly speculative modest versions of panspermia, developed recently, issue whether multiple noogenesis events are possible for instance by Wallis and Wickramasinghe (2004) concurrently or successively at the same ). or Napier (2004), have significant capacity for in- All physical mechanisms of resetting the astro- biological clock on an average habitable planet are fluencing and directly shaping the astrobiological subsumed into a single value of the probability Q. landscape. Since the probability of occurrence of We notice that for small values of Q we recover the panspermia is strongly dependent on the spatial naive SETI optimism of the ”Galactic Club” era of scales, our 1-D model cannot take it into account, 1960s and 1970s, where a sort of monolithic assent but more sophisticated models will undoubtedly need toward Galaxy full of intelligent species and, conse- to incorporate the possibility of such (constructive) quently, viable SETI targets can be perceived. In the local interaction. Various regulation mechanisms are not mutu- other limiting case, when Q → 1, we obtain the most ally exclusive. On the contrary, they are additive interesting case of truly temporally correlated ages and mutually reinforcing. This is a sort of situation for biogenesis and noogenesis. Thus, the toy model quite usual in terrestrial ecology. For instance, a ma- counts only planets achieving noogenesis (emergence jor parameter of terrestrial biosphere is the rate of of intelligent observers) at least once and it does release of carbon. It is influenced by several quite not take into account any subsequent destructive distinct processes; e.g. higher temperatures increase processes, either natural or intelligence-caused (like soil respiration rates, releasing organic carbon stored nuclear, biotech or nanotech self-destruction). As in soils, creating a positive feedback loop. In the Q → 1 the overall number of planets with achieved same time, an increase in frequency of forest fires noogenesis is decreasing, reaching maxima around 5 leads to net replacement of older, larger trees by the Gyr (Fig. 1, lower panel). Although the absolute val- younger, smaller ones, resulting in the net release of ues of N are certainly too high for a realistic model carbon from forest biomass, also creating a positive (main simplification being log-uniform timescale dis- feedback (Woodward, Lomas, and Betts 1998). tribution), the overall picture still reflects the basic trends and sets the stage for further detailed work. We notice that the correlated (”rugged”) land- 4. ASTROBIOLOGICAL LANDSCAPE scape for high Q values (Fig. 1., upper panel) means that there will be a higher ”tier” of devel- A representative prediction of our simplified opment at each local site (neglecting, for the mo- model is shown in Fig. 1 (for technical details, see ment, interaction of sites, especially if we are inter- Papers I and II). Resetting events are taken to be ested in advanced technological civilizations, which GRBs, randomly occurring with exponentially de- cannot be modeled by this approach); this is analo- creasing frequency and the fixed characteristic decay gous of the ”third tier” of terrestrial macroevolution timescale of τ = 3 Gyr, in accordance with the cos- (Gould 1985) comprised of mass extinction episodes mological observations of distant bursts (e.g. Bromm and their effects on the phylogeny of life. Also, and Loeb 2002). The biological timescales for nooge- the maxima at the lower panel of Fig. 1. indicate nesis are randomly sampled from a log-uniform dis- that Earth’s noogenesis timescale is fairly typical, tribution between 108 yrs (the minimum suggested at least for adopted values of relevant Galactic pa- by McKay 1996) and 1016 yrs (the total lifetime rameters. This results in spite of the fact that no specifically ”Copernican” assumption has been built of the Galaxy as a well defined entity; Adams and in the model. As discussed above, this is good news Laughlin 1997). We limit our model to the stellar for practical SETI, since it means that there is a population of the Milky Way thin disk, the age of significant number of potential search targets within which is set, for simplicity, to ttdisk = 10 Gyr. We use the same tier Earth’s biosphere and human civiliza- the age distribution of terrestrial planets calculated tion belong. Of course, the real landscape is much on the basis of chemical evolution by Lineweaver more complex and irregular (even the assumption (2001) as our input data. Probability Q measuring of unique value of Q for any particular history is conveniently averaged severity of the resetting events gross simplification); hopefully, these results will pro- can be regarded as both (1) a geometrical probabil- voke further work on theoretical grounding of SETI ity of an average habitable planet being in the ”lethal projects.

75 B. VUKOTIC´ and M. M. CIRKOVI´ C´

N

1e+09 1e+09 1e+08 1e+08 1e+07 1e+07 1e+06 1e+06 1e+05 1e+05 1e+04 1e+04 1000 1000 100 100 10 10 1 1 0.1 0.2 0.3 0.4 0.5 10000 Q 0.6 9000 8000 0.7 7000 6000 0.8 5000 4000 0.9 3000 2000 1000 1 0 Age of the Thin Disk [Myr]

1e+07

1e+06

1e+05 N 1e+04

1e+07 1000 9e+06 100 8e+06 7e+06 10 6e+06 1 5e+06 4e+06 0 0.1 3e+06 0.2 0.3 2e+06 0.4 0.5 1e+06 0.6 Q 0 0.7 0.8 2.7 2.9 3.1 3.3 0.9 3.5 3.7 1 3.9 4.1 log(t[Myr])

Fig. 1. Astrobiological landscape in 1-D simplified models with GHZ comprising 109 habitable sites. Upper panel: number of planets that have achieved noogenesis at least once (cumulative plot); lower panel: number of planets with elapsed time t between planet formation and completion of noogenesis.

76 NEOCATASTROPHISM AND THE MILKY WAY ASTROBIOLOGICAL LANDSCAPE

5. DISCUSSION AND FUTURE PLANS automata models it would be quite easy to imple- ment the interstellar interactions between the sites, either in forms of naturally-occurring panspermia, or One might argue here that we should not con- – from the point of view of Fermi’s paradox especially sider ”indiscriminative” SETI, but apply some other interesting – interstellar colonization. This would be constraints in order to assess its meaningfulness. in accordance with the general physical usage of the Here, one may again use some of the ammunition of cellular automata models for simulating those com- contact pessimists against them. In contrast to naive plex dynamical systems where local interactions are contact optimism, we are certainly not entitled to in- simple while the whole system is both too large and vest money and effort into attempts at communica- too sensitive to the initial conditions for the direct tion with intelligent societies of any age. The lower approach to be worthwhile. (In astrobiology we need limit of age (the development of radio and/or sim- to add another layer of difficulty to this, since we ilar devices for long-range communication) is taken are in fact lacking knowledge on the details of ”lo- explicitly into account in the Drake equation, but the cal dynamics”, namely biogenesis and noogenesis on anthropic reasoning indicates that we are mistaken terrestrial planets in GHZ.) As an example of the ef- into not taking into account the upper limit as well. fect which would be natural to model within the 3-D In the opinion of the present authors (elaborated in framework is the ”substructure” within GHZ formed ´ by, for instance, nonlinear proportionality between Cirkovi´cand Vukoti´c2008), it is preposterous to as- the local at any given epoch and the prob- sume that SETI can be meaningfully aimed at hy- ability of a star having planets (of any kind).1 pothetical societies 1 Gyr (say) older than ours. 1 In a sense, there is a deeper logic in the succes- Gyr ago, there were no multicellular organisms on sive application of these classes of models for resolv- Earth. There are no more reasons to expect beings 1 ing the long-standing arguments of SETI sceptics. Gyr older than us to communicate with us using ra- While Carter’s anthropic argument was essentially a dio (or anything even remotely similar) than there is 1-D problem (only the number of inhabited planets reason to try to establish dialogue with procaryotes. at given epoch mattered), Fermi’s paradox is essen- However, if the ages of inhabited planets are to a large degree correlated, this obstacle dissolves. We tially 3-D problem (spatial extent of civilizations at have clustering of ages of biospheres around particu- given epoch). Thus, the toy 1-D model can serve to lar values and, possibly, clustering of ages of techno- undermine Carter’s argument (as shown in Cirkovi´c´ logical civilizations (and, thus, viable SETI targets) et al. 2008), but a stronger class of models is neces- as well. This immediately undermines Carter’s ar- sary in order to do the same with Fermi’s paradox. gument for the uniqueness of (as shown in We shall investigate whether 3-D cellular automata more detail in Cirkovi´cet´ al. 2008), but it also opens models are up to the task in a subsequent work. In wide space for ingenuity in the field of practical SETI particular, phase transitions are common phenom- efforts. In this manner, advances in theoretical un- ena in nonlinear systems studied thus far with help derstanding of rather new context can pave the way of probabilistic cellular automata (e.g. Kaneko and for prolonged technical and experimental work, as Akutsu 1986). Finally, in order to face the hardest happened many times in the history of . of all skeptical arguments, the argument from bio- In the course of the future work, we intend logical contingency, one needs additional complexity to apply a different strategy, namely the probabilis- stemming from the parameters determining the size tic cellular automata models, which could in con- of the relevant parts of evolutionary morphospace. It trast to the present model give us more realistic 2- is unclear at present how one could quantify such a D and 3-D pictures of the GHZ evolution. Cellular situation, but it is to be hoped that the rapid devel- automata are spatially extended nonlinear dynam- opment of astrobiological modeling will be up to the ical systems with a huge variety of dynamical be- task. haviors, especially convenient for modeling systems containing a large number of locally interacting sim- ilar components; this immediately brings in mind Acknowledgements – We thank Brian Thomas, stellar systems in general, and Milky Way and its George Dvorsky, Ivana Dragi´cevi´c, Slobodan GHZ in particular. Although a vague precursor of Popovi´c, Tanja Beri´c, Robert J. Bradbury, Sanja such an approach exists in the work of Landis (1998) Eri´c,, and an anonymous referee on application of the to solving for insightful comments and pleasant discussions of Fermi’s paradox, no systematic investigation of this some of the relevant topics. This study has been sup- class of astrobiological models have been performed ported by the Ministry of Science of the Republic thus far. It is clear that this would be complemen- of Serbia through the project No. 146012, ”Gaseous tary to the 1-D models presented here. In the cellular and stellar components of galaxies: interaction and evolution”.

1We acknowledge an anonymous referee for bringing our attention to this important effect. 77 B. VUKOTIC´ and M. M. CIRKOVI´ C´

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NEOKATASTROFIZAM I ASTROBIOLOXKI PEJZA MLEQNOG PUTA

B. Vukoti´cand M. M. Cirkovi´c´

Astronomical Observatory Belgrade, Volgina 7, 11160 Belgrade, Serbia E–mail: [email protected]

UDK 52–37 Prethodno saopxtenje

Broj i raspodela nastanjivih plane- davajue gradualistiqke na preovladavajue ta u Mleqnom putu jedan je od najznaqaj- (neo)katastrofiqku istoriju naxe Galaksije nijih problema savremenih astrobioloxkih vodi do nastanka korelacija izmeu nasta- istraivanja. Ovde istraujemo efekte njivih lokacija na velikoj skali, qime se promene opxte neokatastrofiqke paradigme otvaraju mogunosti rexavanja tako vanih na evoluciju Galaktiqke nastanjive zone. U problema kakvi su Karterov ”antropiqki” ovom radu, ispitujemo granice jednostavnih, argument i Fermijev paradoks. Uz to, raz- 1-dimenzionalnih astrobioloxkih modela matramo mogunosti proxirenja sadaxnje i razmatramo ulogu regulacionih meha- klase modela na prostorno realistiqni 3- nizama u oblikovanju ”astrobioloxkog pejza- dimenzionalni sluqaj korixenjem proba- a”. Pokazujemo kako tranzicija sa preovla- bilistiqkih celularnih automata.

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